How to make layout panel for addon in the render properties window visible only for EEVEE?
Mix in class

Following on from  your answer, 
 can also create a mix in class.  An example below.

The EeveeBasePanel mix in class will make any panel inheriting it be in properties, render context, default closed and poll when the render engine is eevee.

This comes in handy if you are going to register other panels. For example I have put a test panel in the scene context, that will also be in properties,  default hidden and only poll if the render engine is eevee.

Seeing as it seems to be eevee based didn't worry about having compat engines list, or setting the category (tabbed by context rather than category in properties)

import bpy


class MyEeveeAddon(bpy.types.PropertyGroup):

    use_myeevee_addon: bpy.props.BoolProperty(
        name="",
        description="Enable My Eevee Addon",
        default=False
    )
    mea_int_property: bpy.props.IntProperty(
        name="Quality",
        description="Increase My Eevee Addon quality",
        default=8,
        min=0,
        max=128
    )


class EeveeBasePanel:
    bl_space_type = 'PROPERTIES'
    bl_region_type = 'WINDOW'
    bl_context = "render"
    bl_options = {'DEFAULT_CLOSED'}

    @classmethod
    def poll(cls, context):
        return (context.engine == 'BLENDER_EEVEE')


class RENDER_PT_my_eevee_addon(EeveeBasePanel, bpy.types.Panel):
    """Creates a Panel in the render properties window"""
    bl_label = "My Eevee Addon"
    bl_idname = "RENDER_PT_true_mb"


    def draw(self, context):
        layout = self.layout
        scene = context.scene

        col = layout.column(align=True)
        col.prop(scene.me_addon, "mea_int_property")
        col.active = scene.me_addon.use_myeevee_addon

    def draw_header(self, context):
        layout = self.layout
        scene = context.scene

        col = layout.column(align=True)
        col.prop(scene.me_addon, "use_myeevee_addon")

class SCENE_PT_test(EeveeBasePanel, bpy.types.Panel):
    bl_label = "My Eevee Scene Test"
    bl_context = "scene"

    def draw(self, context):
        self.layout.label(text="Test")


classes = (MyEeveeAddon,
           RENDER_PT_my_eevee_addon,
           SCENE_PT_test)


def register():
    for cls in classes:
        bpy.utils.register_class(cls)
    bpy.types.Scene.me_addon = bpy.props.PointerProperty(type=MyEeveeAddon)


def unregister():
    for cls in revrersed(classes):
        bpy.utils.register_class(cls)

if __name__ == "__main__":
    register()